Overlap–save method: Difference between revisions

Revision as of 22:10, 6 November 2020

Revision as of 01:19, 7 November 2020

Line 29:

:<math>y[n] = \sum_{m=1}^{M} h[m] \cdot x_k[n-kL-m] \ \ \triangleq \ \ y_k[n-kL].</math>

With the substitution &nbsp;{{mvarmath|j}} ≜ <math>n-kL</math>}},&nbsp; the task is reduced to computing {{math|y{{sub|k}}(j)}}, for '''''M''''' &nbsp;≤&nbsp; {{mvar|j}} &nbsp;≤&nbsp; '''''L''&nbsp;+''&nbsp;M''&nbsp;−&nbsp;1'''. These steps are illustrated in the first 3 traces of Figure 1, except that the desired portion of the output (third trace) corresponds to '''''1''''' &nbsp;≤&nbsp; {{mvar|j}} &nbsp;≤&nbsp; '''''L''.{{efn-ua

|Shifting the undesirable edge effects to the last M-1 outputs is a potential run-time convenience, because the IDFT can be computed in the <math>y[n]</math> buffer, instead of being computed and copied. Then the edge effects can be overwritten by the next IDFT.&nbsp; A subsequent footnote explains how the shift is done, by a time-shift of the impulse response.}}